covert 2068 twelve to base 10
What base is it in now?
the question reads
covert the numeral to a numeral in base 10
2068
12
For 206812 converted to base 10, you would do the following sum:
2*12^3+
0*12^2+
6*12^1+
8*12^0
=2*1728 + 0*144 + 6*12 + 8*1
= ?
So it is now in base 12 ??
powers of 12:
12, 144, 1728, ...
206812 = 2(12^3) +0(12^2) + 6(12) + 8
= 3456 + 0 + 72 + 8 = 353610
To convert the number "2068" from base 12 to base 10, you need to understand the positional notation of each digit in base 12.
In base 12, each digit's position represents a power of 12. The rightmost digit represents 12^0 (which is equal to 1), the next digit to the left represents 12^1, the next digit represents 12^2, and so on.
Let's break down the number 2068 in base 12:
Starting from the rightmost digit:
8 x 12^0 = 8 x 1 = 8
6 x 12^1 = 6 x 12 = 72
0 x 12^2 = 0 x 144 = 0
2 x 12^3 = 2 x 1728 = 3456
Now, sum up these values:
8 + 72 + 0 + 3456 = 3536
Therefore, the number "2068" in base 12 is equal to 3536 in base 10.